Flemming Holtorf

**_A Brief Update_** The current state of the draft appears to be working quite well and in my opinion already provides some useful functionality. Below you can see an example...

Hey, any thoughts on this @ChrisRackauckas @bowenszhu? The basic functionality of generating PCE moment equations works quite nicely and robustly for polynomial explicit ODE models (see example above). In the...

POD is really at the end of the day not much more than computing (in some clever way) the SVD of a data matrix. For POD to be really really...

This paper focuses on the computational aspects of DO (a lot more approachable than the paper Chris linked which is very theoretical!). For me this was the best reference to...

Some (probably the most basic) version of balanced truncation is already implemented in ControlSystems.jl. You can refer to that implementation to get started. https://juliacontrol.github.io/ControlSystems.jl/latest/lib/analysis/#ControlSystems.baltrunc-Tuple{ST}%20where%20ST%3C:AbstractStateSpace

Very concise and approachable description (and improves Wilcox and Peraire's work from an algorithmic standpoint!) https://www.worldscientific.com/doi/abs/10.1142/S0218127405012429

These are really all variations/extensions/relatives of DMD at the end of the day (lots of stuff related to DMD is already implemented in [https://github.com/SciML/DataDrivenDiffEq.jl](DataDrivenDiffEq.jl)). So consider peaking there for inspiration....

Remarkably good review for everything around non-intrusive PCE: https://arc.aiaa.org/doi/abs/10.2514/6.2009-2274 Almost everything todo with generating a polynomial basis and numerical integration is supported by [PolyChaos.jl](https://github.com/SciML/PolyChaos.jl) but what is really missing is...

Thanks for the quick reply! > I'm not sure what that means. What's "stationarity"? Stationarity is just jargon for a condition that encodes if a point is a stationary point...

> Are you on slack ? I am! Should I ask in some channel there?